There are many, many reasons why a site might work in one browser but not another. In order to troubleshoot this, you need to be more specific as to what's failing.
In addition to the aforementioned web developer bias/blinkers, there could be network-related issues or setups on your machine that are impacting.
For example, Safari uses the OS-specific proxy server settings while Chrome uses its own settings.
If you're using a proxy server, it may be that the proxy server your OS (and therefore Safari) are using is somehow blocking the site, while Chrome is using some other proxy (or no proxy at all).
Proxy servers aren't common for most users, but are common in corporate/enterprise environments. You can check if you're using any proxies via Safari -> Settings -> Advanced -> Proxies.
You may also be configured to use iCloud Private Relay, which funnels all traffic from Safari through Apple's servers to help shield your identity/location from the sites you're visiting. Chrome doesn't use this, so it may be the site is blocking Apple's Private Browsing for some reason. Check System Settings -> Apple Account -> iCloud -> Private Relay to see if this is the issue.
If neither of these help there are ways to dig a little deeper. It's even possible to set Safari to masquerade as Chrome to help bypass developer bias (it doesn't make Safari work like Chrome, it just identifies itself as Chrome to the server, but if there is some Chrome-specific code on the site it may still fail).
Digging even deeper you can use the web inspector built into Safari to trace activity accessing a site. This can help narrow down potential bottlenecks and blocks. We can dig into those if none of the above helps.